A120504 Generalized meta-Fibonacci sequence a(n) with parameters s=1 and k=3.

1, 1, 2, 3, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 18, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 27, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 36, 36, 37, 38, 39

Offset

1,3

Links

Table of n, a(n) for n=1..60.

C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences, J. Integer Seq., Vol. 12. [This is a later version than that in the GenMetaFib.html link]

C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences

Formula

If 1 <= n <= 2, a(n)=1. If 3 <= n <= 4, then a(n)=n-1. If n>4 then a(n)=a(n-1-a(n-1)) + a(n-2-a(n-2)) + a(n-3-a(n-3)).

G.f.: A(z) = z * sum(prod(z * (1 - z^(3 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (3^i - 1) / 2.

Maple

a := proc(n)
option remember;
if n <= 2 then return 1 end if;
if n <= 4 then return n-1 end if;
return add(a(n - i - a(n - i)), i = 1 .. 3)
end proc

Crossrefs

Cf. A120515, A120526.

Sequence in context: A296816 A064474 A072688 * A025772 A211535 A029069

Adjacent sequences: A120501 A120502 A120503 * A120505 A120506 A120507

Keyword

nonn

Author

Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006

Status

approved